A flexible robot arm control method and system based on fuzzy PID

Abstract

The application relates to a flexible mechanical arm control method and system based on a fuzzy PID, and the method comprises the following steps: constructing a flexible mechanical arm dynamics model according to mechanical arm related parameters, a hypothetical modal method and a Lagrange method; decoupling the flexible mechanical arm dynamics model to generate a slow variable subsystem model and a fast variable subsystem model; establishing an extended state observer according to the slow variable subsystem model and an impfal function and generating an observed disturbance value; generating an improved linear sliding mode surface according to a flexible mechanical arm position tracking error and a state power item; deriving the improved linear sliding mode surface to generate a sliding film control law; generating a trajectory tracking control law according to the observed disturbance value and the sliding film control law; generating a vibration suppression control law according to the fast variable subsystem model, a fuzzy PID control algorithm and a mechanical arm end vibration amount; and combining the trajectory tracking control law and the vibration suppression control law to generate a total control law. The method has better anti-disturbance performance and vibration suppression performance.

Description

Technical Field

[0001] This invention relates to the field of industrial production technology, and in particular to a flexible robotic arm control method and system based on fuzzy PID. Background Technology

[0002] Flexible robotic arms possess advantages such as light weight, high efficiency, and low energy consumption, but they also face challenges related to strong coupling and complex modeling. Due to the use of flexible materials, the arm exhibits high-frequency elastic vibrations during movement, which constitutes the coupling characteristic of flexible robotic arms. Because the modes of these high-frequency vibrations are infinite-dimensional, and these elastic vibrations are difficult to quantify and analyze precisely, establishing an accurate mathematical model of the system is challenging. In addition to internal uncertainties, flexible robotic arm systems also experience various external disturbances. Therefore, overcoming the influence of internal and external uncertainties to achieve high-precision, high-steady-state, and high-robust control of the flexible robotic arm has always been a research hotspot. Against this backdrop, selecting appropriate modeling methods and designing suitable control strategies are of significant theoretical and practical value in improving the control performance of flexible robotic arms and enhancing their disturbance resistance.

[0003] When a flexible robotic arm moves, its motion is a rigid-flexible coupling process. It requires precise tracking of the desired trajectory while simultaneously suppressing elastic vibrations to ensure control performance. Existing control methods for flexible robotic arms are numerous, but primarily involve designing controllers directly for the coupled model of the system. Commonly used control methods include SMC control, ADRC control, and fuzzy control. This strategy, which designs the controller for the entire coupled model, not only ignores the coupling characteristics of the flexible robotic arm but also suffers from complex design and high computational cost. While it can track the desired trajectory, the tracking effect is poor due to the lack of suppression of elastic vibrations in the arm. This control strategy uses a single control method, which cannot adequately meet the complex requirements of the robotic arm system. Furthermore, its control objectives lack specificity; it cannot effectively track the trajectory or suppress vibrations, resulting in low system robustness.

[0004] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] Therefore, the technical problem to be solved by the present invention is to overcome the problem that the existing technology has low robustness because the control target is not specific enough, so it cannot track the trajectory well or suppress vibration.

[0006] To address the aforementioned technical problems, a first aspect of the present invention provides a flexible robotic arm control method based on fuzzy PID control, the method comprising:

[0007] Obtain relevant parameters of the robotic arm; the relevant parameters of the robotic arm include: robotic arm length, robotic arm end-effector load mass, robotic arm rotation angle, and robotic arm end-effector vibration.

[0008] A dynamic model of the flexible robotic arm is constructed based on the relevant parameters of the robotic arm, the hypothetical modal method, and the Lagrange method.

[0009] The dynamic model of the flexible robotic arm is decoupled according to the singular perturbation method to generate a slow-variable subsystem model and a fast-variable subsystem model.

[0010] An extended state observer is established based on the slow-varying subsystem model and the impfal function, and observed perturbation values ​​are generated.

[0011] Generate a traditional linear sliding surface based on the position tracking error of the flexible robotic arm;

[0012] An improved linear sliding surface is generated based on the traditional linear sliding surface and the state power term;

[0013] Differentiating the improved linear sliding surface generates the sliding control law;

[0014] A trajectory tracking control law is generated based on the observed disturbance value and the synovial control law;

[0015] Based on the fast-change subsystem model, fuzzy PID control algorithm, and the vibration amount at the end of the robotic arm, a vibration suppression control law is generated.

[0016] The trajectory tracking control law and the vibration suppression control law are combined to generate the overall control law.

[0017] In one embodiment of the present invention, the calculation formula for the robotic arm dynamics model is as follows:

[0018]

[0019] in, Let H be the positive definite mass matrix, H be the cross-coupling matrix, C be the damping matrix, K be the stiffness matrix, and q = [q1 q2…q n ] T The modal coordinates are used to describe the elastic vibration of the flexible robotic arm. w represents the external disturbance, and |w| < d, where d is a positive real number, u is the system input, and θ is the rotation angle of the robotic arm.

[0020] In one embodiment of the present invention, the formula for the slowly varying subsystem model is as follows:

[0021] θ s&& =J(u s +w s -H 1s )

[0022] in, Where N 11s N 12s N 21s N 22s For N s The matrix elements, θ s u is an estimate of θ. s w is the control variable for the slow-varying subsystem. s For external disturbances, H 1s =H1.

[0023] In one embodiment of the present invention, the formula for the fast-changing subsystem model is as follows:

[0024]

[0025] Where d is a positive real number, z f =zz s , t p =t / μ, K s For the new state variable, u f For the control quantity of the fast variable subsystem, F 11s is a coefficient.

[0026] In one embodiment of the present invention, the formula for the improved linear sliding surface is as follows:

[0027]

[0028] Where k1>0, k2>0, k1 and k2 are sliding surface parameters, e s This refers to the position tracking error of the flexible robotic arm.

[0029] In one embodiment of the present invention, the formula of the trajectory tracking control law is as follows:

[0030]

[0031] Where k1 and k2 are sliding surface parameters, k3 and k4 are superhelical parameters, and e s For the position tracking error of the flexible robotic arm, θ d The desired trajectory.

[0032] In one embodiment of the present invention, the formula for the vibration suppression control law is as follows:

[0033]

[0034] Among them, ef The error between the actual value and the target value is given by f, where f is the sampling time and k is the value. p k i and k d These are PID parameters.

[0035] A second aspect of the present invention provides a flexible robotic arm control system based on fuzzy PID, which is applied to a method proposed in any one of the first aspects above. The system includes: a data acquisition module, a model building module, a first calculation module, and a second calculation module.

[0036] The data acquisition module is configured to acquire relevant parameters of the robotic arm, including: robotic arm length, end-effector load mass, robotic arm rotation angle, and end-effector vibration.

[0037] The model building module is configured to: construct a dynamic model of the flexible manipulator based on the relevant parameters of the manipulator, the assumed modal method, and the Lagrange method; and decouple the dynamic model of the flexible manipulator based on the singular perturbation method to generate a slow-variable subsystem model and a fast-variable subsystem model.

[0038] The first calculation module is configured to: establish an extended state observer and generate observed disturbance values ​​based on the slow-varying subsystem model and the impfal function; generate a conventional linear sliding surface based on the position tracking error of the flexible robotic arm; generate an improved linear sliding surface based on the conventional linear sliding surface and the state power term; differentiate the improved linear sliding surface to generate a sliding control law; and generate a trajectory tracking control law based on the observed disturbance values ​​and the sliding control law.

[0039] The second calculation module is configured to: generate a vibration suppression control law based on the fast-change subsystem model, the fuzzy PID control algorithm, and the vibration amount at the end of the robotic arm; and combine the trajectory tracking control law and the vibration suppression control law to generate a total control law.

[0040] A third aspect of the present invention provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the method described in the first aspect or any possible implementation thereof.

[0041] A fourth aspect of the present invention provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in the first aspect or any possible implementation thereof.

[0042] The technical solution of the present invention has the following advantages compared with the prior art:

[0043] The present invention discloses a flexible robotic arm control method and system based on fuzzy PID. By constructing an impfal function, it achieves a smoother surface with better convergence and helps to suppress chattering. The improved sliding surface has a faster convergence speed than the linear sliding surface. The combination of trajectory tracking control law and vibration suppression control law results in better tracking performance, disturbance rejection performance and vibration suppression performance. Attached Figure Description

[0044] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0045] Figure 1 This is a flowchart of a flexible robotic arm control method and system based on fuzzy PID provided by the present invention;

[0046] Figure 2 This is a schematic diagram of a flexible robotic arm control method based on fuzzy PID and a flexible robotic arm model in the system provided by the present invention.

[0047] Figure 3 This is a comparison diagram of the convergence speed of traditional linear sliding surfaces and improved linear sliding surfaces in a flexible robotic arm control method and system based on fuzzy PID provided by the present invention.

[0048] Figure 4 This invention provides a flexible robotic arm control method based on fuzzy PID and a position tracking curve of the flexible robotic arm in the system.

[0049] Figure 5 This invention provides a flexible robotic arm control method based on fuzzy PID and a tracking error curve of the flexible robotic arm in the system.

[0050] Figure 6 This invention provides a flexible robotic arm control method based on fuzzy PID and a combined control output curve diagram in the system.

[0051] Figure 7 This invention provides a flexible robotic arm control method based on fuzzy PID and a sliding mode control output curve diagram in the system.

[0052] Figure 8 This invention provides a flexible robotic arm control method and system based on fuzzy PID, and the end-effector vibration curve of the flexible robotic arm under combined control.

[0053] Figure 9 This invention provides a flexible robotic arm control method based on fuzzy PID and an end-effector vibration curve of the flexible robotic arm under sliding mode control in the system.

[0054] Figure 10 This invention provides a system architecture diagram of a flexible robotic arm control method and system based on fuzzy PID. Detailed Implementation

[0055] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0056] Furthermore, the described embodiments are merely some, not all, of the embodiments of this application. The components of the embodiments of this application described and illustrated herein can typically be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0057] Reference Figure 1 As shown, this invention provides a flexible robotic arm control method based on fuzzy PID, the method comprising:

[0058] S110: Obtain relevant parameters of the robotic arm; the relevant parameters of the robotic arm include: robotic arm length, robotic arm end-effector load mass, robotic arm rotation angle, and robotic arm end-effector vibration.

[0059] In step S110, the selected research object is a single-link flexible robotic arm, one end of which is fixed to the motor shaft, and the other end is connected to a mass load. Its model is referenced. Figure 2 As shown, XOY is the fixed coordinate system, xoy is the reference coordinate system, L is the length of the robotic arm, m is the end load mass of the robotic arm, u(t) is the driving torque, ω(x,t) is the elastic deformation of any point P on the robotic arm at x at time t, and θ(t) is the rotation angle of the robotic arm.

[0060] S111: Construct a dynamic model of the flexible robotic arm based on the relevant parameters of the robotic arm, the assumed modal method, and the Lagrange method;

[0061] In step S111, the calculation formula for the robotic arm dynamics model is as follows:

[0062]

[0063] in, Let H be the positive definite mass matrix, H be the cross-coupling matrix, C be the damping matrix, K be the stiffness matrix, and q = [q1 q2…q n ] TThe modal coordinates are used to describe the elastic vibration of the flexible robotic arm. w represents the external disturbance, and |w| < d, where d is a positive real number, u is the system input, and θ is the rotation angle of the robotic arm.

[0064] In practical applications, a dynamic model of the flexible robotic arm is constructed based on the obtained relevant parameters, the assumed modal method, and the Lagrange method. Since M is positive definite, let... Multiplying both sides of equation (1) by N, we get:

[0065]

[0066] Expanding equation (2) yields:

[0067] θ && =-N 11 H1-N 12 H2-N 12 C q & -N 12 Kq+N 11 (u+w) (3);

[0068] q && =-N 12 H2-N 22 H2-N 22 Cq & -N 22 Kq+N 21 (u+w) (4);

[0069] S112: Decouple the dynamic model of the flexible manipulator according to the singular perturbation method to generate a slow-variable subsystem model and a fast-variable subsystem model;

[0070] In step S112, the formula for the slowly varying subsystem model is as follows:

[0071] θ s && =J(u s +w s -H 1s (5);

[0072] in, Where N 11s N 12s N 21s N 22s For N s The matrix elements, θ s u is an estimate of θ. s w is the control variable for the slow-varying subsystem. s For external disturbances, H 1s =H1. The formula for the rapidly changing subsystem model is as follows:

[0073]

[0074] Where d is a positive real number, z f =zz s , t p =t / μ, K s For the new state variable, u f For the control quantity of the fast variable subsystem, F 11s is a coefficient.

[0075] In practical applications, parameters are introduced based on singular perturbation theory. λ=min{k i}, i = 1, 2, ..., n, introduce a new state variable K s =μ 2 K, z = q / μ 2 Substituting into equations (2) and (3), we get:

[0076]

[0077]

[0078] Let the perturbation parameter μ = 0, and obtain the slow variable component according to equations (4) and (7).

[0079]

[0080] 0 = -N 21s H 1s -N 22s H 2s -N 22s K s z s +N 21s (u s +w s (10);

[0081] Among them, the components with the subscript 's' are the slowing quantities. According to equation (9):

[0082]

[0083] Substituting equation (10) into equation (8), we obtain the slow-varying subsystem model, w s =w, because w s Because the change is slow, it can be assumed that it only exists in slowly varying subsystems. Since θ and q have different time characteristics, a fast timescale t is introduced. p = t / μ, at this time scale, the slow variable can be considered a constant, that is:

[0084]

[0085]

[0086] Let z f =zz s Substituting into equation (7), and combining equations (4), (7), and (5), we obtain the model of the flexible robotic arm's fast-change subsystem.

[0087] According to Tikhonov's theory: θ = θ s +o(μ) (14);

[0088] q=μ(z s +z f )+o(μ) (15);

[0089] Where o(μ) is a higher-order infinitesimal of μ. According to equations (14) and (15), the state of the subsystem differs from the state of the original system only by a higher power of μ. Therefore, the original system can be controlled by designing a control law for the subsystem.

[0090] S113: Establish an extended state observer and generate observed perturbation values ​​based on the slow-varying subsystem model and the impfal function;

[0091] In step S113, for the slowly varying subsystem represented by equation (5), its state-space equation can be expressed as:

[0092]

[0093] Where x1 = θ, b = J, f = J(w) s -H 1s Define the extended state x3 = f, and denote it as f. Subsystem (16) can then be expanded into the following system:

[0094]

[0095] Establish an extended state observer for the system of equation (17):

[0096]

[0097] Its discrete form is as follows:

[0098]

[0099] Where e is the observation error, y is the system output, h is the integration step size, z1 is the system output observation, z2 is the output differential observation, z3 is the disturbance observation, and β 01 ,β 02 ,β 03Here, αl represents the observer filter coefficients, b represents the controller gain (b = J), and α1, α2, and δ are adjustable parameters. The specific form of the fal function is as follows:

[0100]

[0101] The fal function is the core of ESO, and its essence is a mathematical fit to "large error, small gain; small error, large gain". α determines the linearity of the fal function, and δ determines the length of the linear interval of the function. As shown in equation (20), the fal function is continuous but not differentiable when |e|=δ. The sudden change in the derivative will cause oscillations and affect the system performance. At the same time, when |e|>1, if α is large, the final system gain may still be very large, which does not meet the requirement of "large error, small gain". In order to solve the above problems and improve the system performance, the improved fal function needs to satisfy: the function is symmetric about the origin and differentiable everywhere, and satisfies the requirement of "large error, small gain; small error, large gain".

[0102] When |e|≤δ, the improved fal function uses a combination of trigonometric and power functions for fitting:

[0103] impfal(e,α,δ)=k1sine+k2e 2 +k3tane (21);

[0104] Where k1, k2, and k3 are the gain coefficients. When |e| > δ, to prevent the gain of the fal function from becoming too large when the error is large, a limiting factor λ is introduced:

[0105]

[0106] For the function to be continuous and differentiable when |e|=δ, that is:

[0107]

[0108] Solving the above equation, we get:

[0109]

[0110] In summary, the improved impfal function is as follows:

[0111]

[0112] A comparison of the graphs of the original FAL function and the improved ImpFAL function when α = 0.25, δ = 0.2, and λ = 2. Error gain curves of the original FAL function and the improved ImpFAL function when α = 0.25, δ = 0.2, and λ = 2.

[0113] Based on the above analysis, compared with the fal function, the impfal function has the following advantages: when |e|=δ, the impfal function is continuous and smooth, differentiable, avoiding the chattering problem caused by abrupt changes; when |e|≤δ, the impfal function has a larger gain, better satisfying the requirement of "small error, large gain"; when |e|>1, the impfal function has a smaller gain, better satisfying the requirement of "large error, small gain"; the impfal function can have better robustness by adjusting the value of λ to control the gain.

[0114] The improved extended state observer is:

[0115]

[0116] To prove the stability of ESO, the error equation of ESO can be obtained from equations (17) and (26):

[0117] e & (t)=-A(e(t))e(t) (27);

[0118] in:

[0119]

[0120] If there exists a matrix whose main diagonal elements are all positive numbers. make If the system is positive definite and symmetric, then the zero solution of the system (27) is asymptotically stable by Lyapunov.

[0121] in,

[0122] To satisfy DA(e) as positive definite symmetric, that is:

[0123] d 22 =-d 13 D 31 =-d 12 D 21 =-d 11 (29);

[0124] D 11 >0 (30);

[0125]

[0126]

[0127] Let d 11 =1,d 22 =d 23 =ε (ε→0) +Then equations (30), (31), and (32) are equivalent to:

[0128]

[0129]

[0130]

[0131] Where B = β 01 β 02 -β 03 The above formula holds true when B > 0.

[0132] If the observer's filter coefficient β 01 ,β 02 and β 03 Satisfy β 01 β 02 -β 03 If the value is greater than 0, a matrix D that satisfies the above requirements can be constructed to make DA(e) positive definite and symmetric. Then the zero solution of system (27) is Lyapunov asymptotically stable.

[0133] S114: Generate a traditional linear sliding surface based on the position tracking error of the flexible robotic arm;

[0134] In step S114, the position tracking error of the flexible robotic arm is defined as follows:

[0135] e s =θ d -θ (36);

[0136] Where, θ d Let θ be the desired angular displacement and θ be the actual angular displacement. Based on the position tracking error e... s The traditional linear sliding surface is:

[0137]

[0138] Where k > 0 are the sliding surface parameters.

[0139] S115: Generate an improved linear sliding surface based on the traditional linear sliding surface and the state power term;

[0140] In step S115, the formula for the improved linear sliding surface is as follows:

[0141]

[0142] Where k1 > 0, k2 > 0, k1 and k2 are sliding surface parameters, e s This refers to the position tracking error of the flexible robotic arm.

[0143] In practical applications, to improve the convergence speed of errors on the sliding surface, a state power term is added, improving the sliding surface as shown in equation (38). (Refer to...) Figure 3 The image shows a comparison of the convergence rates of a traditional linear sliding surface and an improved linear sliding surface. Figure 3 It can be seen that the convergence speed of the systematic error on the improved linear sliding surface is better than that on the traditional linear sliding surface.

[0144] S116: Differentiate the improved linear sliding surface to generate the sliding control law;

[0145] In step S116, taking the derivative of equation (38) and combining it with equation (5), we have:

[0146]

[0147] S117: Generate a trajectory tracking control law based on the observed disturbance value and the sluice control law;

[0148] In step S117, the formula for the trajectory tracking control law is as follows:

[0149]

[0150] Where k1 and k2 are sliding surface parameters, k3 and k4 are superhelical parameters, and e s For the position tracking error of the flexible robotic arm, Where N 11s N 12s N 21s N 22s For N s The matrix elements, θ d The desired trajectory.

[0151] In practical applications, the novel superspiral sliding mode control law is designed as follows:

[0152] u s =u eq +u sw (40);

[0153] Among them, u eq For the equivalent control law, u sw To switch control laws.

[0154] Let s & =0, ignoring system disturbances, we obtain the equivalent control law:

[0155]

[0156] The switching control law uses superspin control:

[0157]

[0158] Where k3 > 0, k4 > 0, and k3 and k4 are superspinning parameters. To reduce chattering and optimize control performance, the impfal function is used instead of the sgn function, resulting in the improved switching control law:

[0159]

[0160] From equations (41), (43), and (26), the novel super-spiral sliding mode control law can be obtained as follows:

[0161]

[0162] Constructing Lyapunov functions:

[0163]

[0164] Differentiating the Lyapunov function yields:

[0165]

[0166] V & =0. Therefore, the novel superspiral sliding mode control satisfies the Lyapunov stability condition. Thus, under the action of the novel superspiral sliding mode controller, the slow-varying subsystem becomes asymptotically stable, i.e., s→0 as t→∞.

[0167] S118: Generate a vibration suppression control law based on the fast-change subsystem model, the fuzzy PID control algorithm, and the vibration amount at the end of the robotic arm;

[0168] In step S118, the formula for the vibration suppression control law is as follows:

[0169]

[0170] Among them, e f The error between the actual value and the target value is represented by T, where T is the sampling time and k is the value. p k i and k d These are PID parameters.

[0171] In practical applications, fuzzy PID control uses the system error e as a reference. f and error change rate ec f As a control input, with Δk p Δk i and Δk d For output, the PID parameters are adjusted online using fuzzy control rules:

[0172]

[0173] Where, k p0 k i0 and k d0 k p k i and k d The initial value of e. f ec f Δk p Δk i and Δk d It is divided into 7 fuzzy sets: positive large PB, positive middle PM, positive small PS, zero ZO, negative small NS, negative middle NM, and negative large NB, denoted as {NB, NM, NS, ZO, PS, PM, PB}. NB and PB use Z-shaped and S-shaped membership functions respectively, while the rest use triangular membership functions. f The domain of discourse is [-3, 3], ec f The domain of discourse is [-3, 3], Δk p The universe of discourse is [-0.3, 0.3], Δk i The universe of discourse is [-0.06, 0.06], Δk d The domain of discourse is [-3, 3].

[0174] The self-tuning principle of PID parameters is as follows: If e f and EC f Since the input signal is relatively large, k can be appropriately increased to ensure the system's response speed to the input signal. p and decrease k d Meanwhile, to prevent the impact of integral saturation on the system, k can be appropriately reduced. i If e f and EC f When the overshoot is moderate and the system overshoot is large, k can be appropriately reduced. p and k d To reduce overshoot, and to ensure the system's response speed to input signals, an appropriate k should be selected. i If e f and EC f If it's too small, you can increase k. p and k i To ensure system stability, and at the same time k d The value should be appropriate to avoid unnecessary oscillations in the system.

[0175] S119: Combine the trajectory tracking control law and the vibration suppression control law to generate a total control law.

[0176] In step S119, the trajectory tracking control law and the vibration suppression control law are combined to obtain the overall control law:

[0177] u(t)=u s(t)+u f (t) (49);

[0178] Among them, u s (t) represents the trajectory tracking control law, u f (t) represents the vibration suppression control law. Under the condition that all the above conditions are met, the trajectory tracking controller and the vibration suppression controller can respectively make the slow-changing subsystem and the fast-changing subsystem asymptotically stable.

[0179] To verify the performance of the designed combined controller, simulations were performed in MATLAB. Table 1 shows the parameters of the flexible robotic arm, and Table 2 shows the controller parameters.

[0180] Table 1:

[0181] parameter symbol numerical values unit length L 1.5 m width b 0.1 m thickness h 0.07 m density ρ <![CDATA[2.81×10 3 ]]> <![CDATA[kg / m 3 ]]> End quality m 4 kg elastic modulus E <![CDATA[0.72×10 11 ]]> <![CDATA[N / m 2 ]]> Moment of inertia Jh 1 <![CDATA[kg / m 2 ]]>

[0182] Table 2:

[0183]

[0184] To simultaneously verify the tracking performance and disturbance rejection performance of the novel superspiral sliding mode control based on improved ESO compared to traditional linear sliding mode control, as well as the vibration suppression performance of the combined control, the desired signal of the flexible robotic arm is θ. d =sin(t), and a sudden disturbance of magnitude 400 N·m is added at the 5th second. The initial state of the flexible robotic arm is θ0 = 0.5 rad, referencing Figure 4 The figure shown is the position tracking curve of the flexible robotic arm, with reference to... Figure 5 As shown, this is the tracking error curve, from... Figure 4 and Figure 5 As can be seen, the novel superspiral sliding mode control outperforms the traditional linear sliding mode control in tracking performance, achieving faster tracking of the desired trajectory. Furthermore, the ESO-based novel superspiral sliding mode control provides better system compensation after disturbances, thus recovering tracking of the desired trajectory more quickly. (Refer to...) Figure 6 The figure shown is the combined control output curve, referencing... Figure 7 The figure shows the output curve of sliding mode control. Figure 6 and Figure 7 As can be seen, the combined control input curve is smoother and the control effect is better, while the sliding mode control suffers from chattering. This is because the sgn function in sliding mode control has abrupt changes, while the impfal function is smoother than the sgn function and has no inflection point. Furthermore, the super-spiral sliding mode applies discontinuous control quantities to higher-order derivatives, thus effectively suppressing chattering. (Refer to...) Figure 8 The figure shows the end effector vibration curve of the flexible robotic arm under combined control, with reference to... Figure 9The figure shows the end effector vibration curve of the flexible robotic arm under sliding mode control. Figure 8 and Figure 9 As can be seen, compared with sliding mode control, combined control has better vibration suppression performance and can suppress elastic vibration more quickly. This is because after the singular perturbation decomposition of the flexible robotic arm, the control target of the system is more precise, thus resulting in better control effect.

[0185] Secondly, referring to Figure 10 As shown, this application provides a flexible robotic arm control system based on fuzzy PID, the system including: a data acquisition module 100, a model building module 200, a first calculation module 300, and a second calculation module 400;

[0186] The data acquisition module 100 is configured to acquire relevant parameters of the robotic arm; the relevant parameters of the robotic arm include: robotic arm length, robotic arm end-load mass, robotic arm rotation angle, and robotic arm end-vibration.

[0187] The model building module 200 is configured to: construct a dynamic model of the flexible manipulator based on the relevant parameters of the manipulator, the assumed modal method, and the Lagrange method; and decouple the dynamic model of the flexible manipulator based on the singular perturbation method to generate a slow-varying subsystem model and a fast-varying subsystem model.

[0188] The first calculation module 300 is configured to: establish an extended state observer and generate observed disturbance values ​​based on the slow-varying subsystem model and the impfal function; generate a conventional linear sliding surface based on the position tracking error of the flexible robotic arm; generate an improved linear sliding surface based on the conventional linear sliding surface and the state power term; differentiate the improved linear sliding surface to generate a sliding control law; and generate a trajectory tracking control law based on the observed disturbance values ​​and the sliding control law.

[0189] The second calculation module 400 is configured to: generate a vibration suppression control law based on the fast-change subsystem model, the fuzzy PID control algorithm, and the vibration amount at the end of the robotic arm; and combine the trajectory tracking control law and the vibration suppression control law to generate a total control law.

[0190] The effects of applying the aforementioned method in the above system can be found in the description of the aforementioned method embodiments, and will not be repeated here.

[0191] A third aspect of the present invention provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the method described in the first aspect or any possible implementation thereof.

[0192] A fourth aspect of the present invention provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in the first aspect or any possible implementation thereof.

[0193] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0194] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0195] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0196] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0197] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A flexible robot arm control method based on fuzzy PID, characterized by, The method includes: Obtain relevant parameters of the robotic arm; the relevant parameters of the robotic arm include: robotic arm length, robotic arm end-effector load mass, robotic arm rotation angle, and robotic arm end-effector vibration. A dynamic model of the flexible robotic arm is constructed based on the relevant parameters of the robotic arm, the hypothetical modal method, and the Lagrange method. The dynamic model of the flexible robotic arm is decoupled according to the singular perturbation method to generate a slow-variable subsystem model and a fast-variable subsystem model. According to the slowly varying subsystem model and The function establishes an extended state observer and generates an observation disturbance value; Generate a traditional linear sliding surface based on the position tracking error of the flexible robotic arm; An improved linear sliding surface is generated based on the traditional linear sliding surface and the state power term; Differentiating the improved linear sliding surface generates the sliding control law; A trajectory tracking control law is generated based on the observed disturbance value and the synovial control law; Based on the fast-change subsystem model, fuzzy PID control algorithm, and the vibration amount at the end of the robotic arm, a vibration suppression control law is generated. The trajectory tracking control law and the vibration suppression control law are combined to generate the overall control law; The formula for the improved linear sliding surface is as follows: in, , , and For sliding surface parameters, This refers to the position tracking error of the flexible robotic arm. The formula for the trajectory tracking control law is as follows: in, and For sliding surface parameters, and For superhelical parameters, For the position tracking error of the flexible robotic arm, z3 represents the desired trajectory; z3 represents the observed disturbance value. ,in for Matrix elements.

2. The flexible robotic arm control method based on fuzzy PID according to claim 1, characterized in that, The calculation formula for the robotic arm dynamics model is as follows: in, It is a positive definite mass matrix. This is a cross-coupling matrix. Here is the damping matrix. Here is the stiffness matrix. To describe the modal coordinates of the elastic vibration of the flexible robotic arm, External disturbances, and , It is a positive real number. For system input, This refers to the rotation angle of the robotic arm.

3. The flexible robotic arm control method based on fuzzy PID according to claim 1, characterized in that, The formula for the slowly varying subsystem model is as follows: in, ,in for matrix elements, for The estimated value, For the control quantity of the slow-varying subsystem, External disturbances .

4. The flexible robotic arm control method based on fuzzy PID according to claim 1, characterized in that, The formula for the rapidly changing subsystem model is as follows: in, It is a positive real number. , , For the new state variables, For the control quantity of the fast variable subsystem, is a coefficient.

5. The flexible robotic arm control method based on fuzzy PID according to claim 1, characterized in that, The formula for the vibration suppression control law is as follows: in, This represents the error between the actual value and the target value. Sampling time, , and These are PID parameters.

6. A flexible robotic arm control system based on fuzzy PID, characterized in that, The flexible robotic arm control method based on fuzzy PID, applied to any one of claims 1 to 5, comprises: a data acquisition module, a model building module, a first calculation module, and a second calculation module; The data acquisition module is configured to acquire relevant parameters of the robotic arm, including: robotic arm length, end-effector load mass, robotic arm rotation angle, and end-effector vibration. The model building module is configured to: construct a dynamic model of the flexible manipulator based on the relevant parameters of the manipulator, the assumed modal method, and the Lagrange method; and decouple the dynamic model of the flexible manipulator based on the singular perturbation method to generate a slow-variable subsystem model and a fast-variable subsystem model. The first calculation module is configured to: calculate based on the slowly varying subsystem model and The function establishes an extended state observer and generates observed disturbance values; it generates a traditional linear sliding surface based on the position tracking error of the flexible robotic arm; it generates an improved linear sliding surface based on the traditional linear sliding surface and the state power term; it differentiates the improved linear sliding surface to generate a sliding control law; and it generates a trajectory tracking control law based on the observed disturbance values ​​and the sliding control law. The second calculation module is configured to: generate a vibration suppression control law based on the fast-change subsystem model, the fuzzy PID control algorithm, and the vibration amount at the end of the robotic arm; and combine the trajectory tracking control law and the vibration suppression control law to generate a total control law.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the flexible robotic arm control method based on fuzzy PID as described in any one of claims 1 to 5.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of a flexible robotic arm control method based on fuzzy PID as described in any one of claims 1 to 5.

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